Course Title:

   Advanced Applied Mathematics I: Modeling

Textbook:

Practical Applied Mathematics, ISBN # 0-521-84274-3, by S.D. Howison, First Edition, Cambridge University Press.

Prerequisites:

Math 331 and Math 337, or departmental approval.

Website:

Course Outline

Week

Lecture

Chapters

Topic

Assignment

1

1,2

1,2

Basics of modeling: Review of some basic modeling principles and derivation/overview of some fundamental models (heat flow, fluid dynamics, wave equation…)

All Homeworks   will be assigned in class.  Some assignments may involve preparing a topic for presentation in class.

2

3,4

2,3

Units, Dimensions, Dimensional analysis: Discussion illustrated by examples from fluid flow and mechanics.

3

5,6

4,5,6

Case Studies: Models arising in industrial applications

4

7,8

7

Partial Differential Equations: Examples; method of characteristics; shocks.

5

9,10

8

Case study: Traffic modeling.

6

11,12

9

Simple distributions: Delta function, Heaviside function and their uses in models.  Simple Green’s functions.

7

13,14

11

Case Study: Pantograph

8

15

      16

12

Midterm Exam

Asymptotic expansions

9

17,18

13

Regular perturbation expansions: Stability analysis; case studies

10

19,20

15

Case study: Piano tuning

11

21,22

16

Boundary layers: Examples from ODEs and PDEs.

12

23,24

Case studies

13

25,26

20

Asymptotic models in fluid dynamic: Case studies, including “thin film” models.

14

27,28

Further modeling

15

29,30

final EXAM

IMPORTANT DATES

Day Sections

Night Sections

FIRST DAY OFCLASSES

                                                   September 4, 2012

Common Exam I

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Common Exam II

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LAST DAY TO WITHDRAW

                                                  November 6, 2012

Common Exam III

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LAST DAY OF CLASSES

                                                   December 12, 2012

FINAL EXAM PERIOD

                                                   December 14-20, 2012

Assignment Weighting

Tentative Grading Scale

Hand-in coursework

40 

A

86 -- 100

Online Homework

none

B+

75 -- 85

Midterm Exam 

30

B

60 -- 74

Final Exam

30

C+

55 -- 64

C

40 - 54

            F

0 - 39